Perhaps I should have said in my OP that I'm not determined to make this setup work; in fact, it was just loaner-wheel situation where I wanted to compare the ride of the brittle, hard-as-rock tires the bike came with the cushy Schwalbes I had sitting around waiting to go back on another project.
But since I also had my little screwdriver with me, I figured, "What the hell, let's see if this old medium cage derailleur likes that big ol' 34T cog" and backing off the screw a turn, was
very surprised that it did. And I was equally surprised it
didn't work with the smaller 13T cog. I spent the next 20 minutes making sure the "high" adjustment on the RD was set to line up the RD to the small cog, back-and-forth, back-and-forth, still no go. Skipping like a little Catholic girl on the way home from Sunday school. "This is ass-backwards," I thought to myself, riding off for a 20 mile jaunt undhindered but for a lack of that top gear.
The "worn cog" theory didn't occur to me, since I bought that freewheel NOS and haven't used it all that much. To my admittedly untrained eye, it looks pretty fresh, but is very skippity on the small (13T) cog, on this bike. On the 3 other bikes I've had it on - all with long cage RDs - it's fine. In fact, it's "SunTour Perfect".
Here's a better photo:
And here's the original 14-28 freewheel, marked Shimano UG, maybe a little more worn? But this is the one that happily works in all gears:
I did an informal tension test with the chain riding the small/small combo, and while it seemed pretty loose, it wasn't visibly sagging and the tension seemed similar to other bikes I have sitting around with the chain on small/small.
Anyway, I thought it'd be a fun thing to bring before the collective wisdom of my fellow C&Vers who are more experienced with this stuff to see what they thought of what I thought was a backwards situation.